Question

A line passes through the points (–2, –8) and (–4, –8). Which shows the graph of this line?
On a coordinate plane, a vertical line is at x = negative 2.
On a coordinate plane, a horizontal line is at y = negative 2.
On a coordinate plane, a vertical line is at x = negative 8.
On a coordinate plane, a horizontal line is at y = negative 8.

Answer 1

To determine the equation of the line that passes through the points \((-2, -8)\) and \((-4, -8)\), we can notice that both points have the same \(y\)-coordinate, which is \(-8\). This indicates that the line is horizontal.

Since the \(y\)-coordinate is constant at \(-8\), the equation of the line can be written as:

\[
y = -8
\]

A horizontal line at \(y = -8\) means that for any value of \(x\), the value of \(y\) will always be \(-8\).

Thus, out of the options provided:

- On a coordinate plane, a vertical line is at \(x = -2\) - **No**
- On a coordinate plane, a horizontal line is at \(y = -2\) - **No**
- On a coordinate plane, a vertical line is at \(x = -8\) - **No**
- On a coordinate plane, a horizontal line is at \(y = -8\) - **Yes**

So the correct answer is: **On a coordinate plane, a horizontal line is at \(y = -8\).**